An innovative approach is represented by Laser – Self – Mixing (LSM) interferometry, which does not require any reference arms or external detectors and it is conveniently replicable because of a robust and almost self-aligned setup, an intrinsic resolution more than adequate for most industrial applications, and a simple and single-channelled reading electronics. Although the LSM has been widely studied and exploited for metrological applications since more than three decades, it has rarely been applied to the simultaneous measurements of more than one DOF.Recently, the authors reported on a compact interferometric system based on the LSM effect, capable of tracking the longitudinal displacement of a target with sub-micron resolution up to 1 meter simultaneously with yaw and pitch rotations up to �� 0.

45�� [9], and with straightness and flatness displacements up to �� 1 mm [10].In this paper, we extend the measurement technique to the evaluation of the roll angle up to �� 0.45��, and we finally present an integrated all-interferometric sensor totally based on the LSM effect for the measurement of six DOFs of a moving target. The described sensor is composed of six laser sources and a suitably designed reflective target, formed by three reciprocally tilted mirrors. The measurement technique is based on the differential measurement of linear displacement by pairs of identical self-mixing interferometers (SMIs), each formed only by a laser diode package with integrated monitor photodiode, a collimated lens, and a reflective surface orthogonal to the optical axis.

Throughout the manuscript, the coordinate convention illustrated in Figure 1 will be adopted:-the x-axis is the direction of linear motion and any displacement along this axis will be indicated by ��x;-the y-axis is the direction of the straightness displacement indicated by ��y;-the z-axis is the direction of the flatness displacement indicated by ��z;-roll is the angular motion around the x-axis and any rotation around this axis will be indicated by ��x;-pitch is the angular motion around the y-axis and any rotation around this axis will be indicated by ��y;-yaw is the angular motion around the z-axis and any rotation around this axis will be indicated by ��z.Figure 1.Coordinate system convention, linear (at the left) and angular (at the right).

The paper is organized as follows: the self-mixing interference GSK-3 principle is introduced in Section 2. The measurement technique for two rotations (yaw and pitch) is reported in Section 3. The extension of the basic principle to the assessment of transverse DOFs is described in Section 4. Considerations about the performance and the integration of the system for the simultaneous measurement of more DOFs are discussed in Section 5 and 6, respectively. Finally, conclusions are drawn in Section 7.2.?Laser-Self-Mixing Interference2.1.